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<H1><A NAME="SECTION03210000000000000000"></A><A NAME="whatisnew"></A>
<BR>
What's new in version 3.0?
</H1>

<P>
Version 3.0 of LAPACK introduces new routines, as well
as extending the functionality of existing routines.  The most significant
new routines and functions are:

<P>
<DL COMPACT>
<DT>1.
<DD>a faster singular value decomposition (SVD),
computed by divide-and-conquer (xGESDD)
 <DT>2.
<DD>faster routines for solving rank-deficient least squares problems:

<UL><LI>using QR with column pivoting (xGELSY, based on xGEQP3)

<LI>using the SVD based on divide-and-conquer (xGELSD)
    
</UL>
 <DT>3.
<DD>new routines for the generalized symmetric eigenproblem:

<UL><LI>xHEGVD/xSYGVD, xHPGVD/xSPGVD, xHBGVD/xSBGVD: faster routines
          based on divide-and-conquer

<LI>xHEGVX/xSYGVX, xHPGVX/xSPGVX, xHBGVX/xSBGVX: routines based on
          bisection/inverse iteration to more efficiently compute
          a subset of the eigenvalues and/or eigenvectors
      
</UL>
 <DT>4.
<DD>faster routines for the symmetric eigenproblem using the
       ``relative robust representation'' algorithm
       (xSYEVR/xHEEVR, xSTEVR, xSTEGR)
 <DT>5.
<DD>new simple and expert drivers for the generalized nonsymmetric
    eigenproblem (xGGES, xGGEV, xGGESX, xGGEVX), including error bounds
 <DT>6.
<DD>a solver for the generalized Sylvester equation (xTGSYL), used in 5)
 <DT>7.
<DD>computational routines (xTGEXC, xTGSEN, xTGSNA) used in 5)
 <DT>8.
<DD>a blocked version of xTZRQF (xTZRZF), and associated xORMRZ/xUNMRZ
</DL>

<P>
One of the primary design features of the LAPACK library is that all
releases are backward compatible.  A user's program calling LAPACK will
never fail because of a new release of the library.  As a result,
however, the calling sequences (or amount of workspace required) to existing
routines cannot be altered.  Therefore, if a performance enhancement requires a
modification of this type, a new routine must be created.  There are
several routines included in LAPACK, version 3.0, that fall into this
category.  Specifically,

<UL><LI>xGEGS is deprecated and replaced by routine xGGES

<LI>xGEGV is deprecated and replaced by routine xGGEV

<LI>xGELSX is deprecated and replaced by routine xGELSY

<LI>xGEQPF is deprecated and replaced by routine xGEQP3

<LI>xTZRQF is deprecated and replaced by routine xTZRZF

<LI>xLATZM is deprecated and replaced by routines xORMRZ/xUNMRZ

</UL>
The ``old'' version of the routine is still included in the
library but the user is advised to upgrade to the ``new'' faster
version.  References to the ``old'' versions are removed from this
users' guide.

<P>
In addition to replacing the above list of routines, there are a number of
other significantly faster new driver routines that we recommend in place of
their older counterparts listed below. We continue to include the older drivers
in this users' guide because the old drivers may use less workspace than the
new drivers, and because the old drivers may be faster in certain special cases
(we will continue to improve the new drivers in a future release until they
completely replace their older counterparts):

<UL><LI>xSYEV/xHEEV and xSYEVD/xHEEVD should be replaced by xSYEVR/xHEEVR

<LI>xSTEV and xSTEVD should be replaced by xSTEVR

<LI>xSPEV/xHPEV should be replaced by xSPEVD/xHPEVD

<LI>xSBEV/xHBEV should be replaced by xSBEVD/xHBEVD

<LI>xGESVD should be replaced by xGESDD

<LI>xSYGV/xHEGV should be replaced by xSYGVD/xHEGVD

<LI>xSPGV/xHPGV should be replaced by xSPGVD/xHPGVD

<LI>xSBGV/xHBGV should be replaced by xSBGVD/xHBGVD

</UL>

<P>
This release of LAPACK introduces routines that exploit IEEE arithmetic.
We have a prototype running of a new algorithm (xSTEGR), which may be the
ultimate solution for the symmetric eigenproblem on both parallel and serial
machines.
This algorithm has been incorporated into the drivers xSYEVR, xHEEVR and xSTEVR
for the symmetric eigenproblem, and will be propagated into the generalized
symmetric definite eigenvalue problems, the SVD, the generalized SVD and the
SVD-based least squares solver.
Refer to section&nbsp;<A HREF="node48.html#subseccompsep">2.4.4</A> for further information.
We expect to also propagate this algorithm into ScaLAPACK.

<P>
We have also incorporated the <I>LWORK</I>=-1 query capability into this
release of LAPACK, whereby a user can request the amount of workspace required
for a routine.  For complete details, refer to section&nbsp;<A HREF="node118.html#lworkquery">5.1.8</A>.

<P>
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<ADDRESS>
<I>Susan Blackford</I>
<BR><I>1999-10-01</I>
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